Primary abelian groups having all high subgroups isomorphic

Cutler, Doyle O.

doi:10.1090/S0002-9939-1981-0627671-7

Primary abelian groups having all high subgroups isomorphic
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by Doyle O. Cutler PDF

Proc. Amer. Math. Soc. 83 (1981), 467-470 Request permission

Abstract:

Let $G$ be a primary abelian group such that $G/{p^\omega }G$ is ${p^{\omega + n}}$-projective for some positive integer $n$, and if $n > 1$ then the $(\omega + m)$ Ulm invariant of $G$ is zero for $0 \leqslant m < n - 1$. We prove that $G$ has the property that all of its high subgroups are isomorphic. An example is given to show that in general the condition on the Ulm invariant is necessary and that this property is not preserved by direct sums.

References

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